In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa).
A weather watch, on the other hand, typically refers to an alert issued to indicate that conditions are favorable for the development of dangerous weather patterns, although the dangerous weather conditions themselves are not currently present.
A tornado watch defines an area where tornadoes and other kinds of severe weather are possible in the next several hours. It means that you need to be alert, and be prepared to go to safe shelter if tornadoes happen or a warning is issued.